Economic Science: Mathematics, Spirituality, Judaism, Christianity, and Islam

 

Since the publication of my book The End of Economic Science, The Beginning of the Golden Age, many of you have asked me to deepen the chapter devoted to sacred mathematics and especially the identity cos²x + sin²x = 1, which escapes the simple scholastic framework. This formula is one of the secret pillars of the universal tradition, a key to reading reality, an exact mirror of the unity that sustains all manifestation.

For this equality is not an abstract construction: it is the beating heart of living geometry. Imagine a point traveling around the circle of radius 1: its horizontal projection, the cosine, is water, receptivity, the feminine horizontality evoked by Sleeping Beauty or Snow White lying down. Its vertical projection, the sine, is fire, the ascending energy of the masculine, that force which rises toward the sky, symbolized by the Olympic flame.

Thus is revealed the fundamental truth that the sages of all traditions have transmitted in a thousand forms: existence rests on two complementary polarities, one horizontal, the other vertical, one feminine, the other masculine, and it is their harmonious union that gives birth to the One. The unit circle does not merely represent a geometric figure; it is the perfect illustration of totality, of the union of opposites, of the balance that sustains creation. And the trigonometric identity that governs it is nothing less than the mathematical signature of this unity.

This chapter, which I develop here, reveals why cos²x + sin²x = 1 is not a simple calculation tool: it is a matrix formula, a schema of the world, a forgotten spiritual key—and yet indispensable for understanding what must collapse and what must be reborn in our civilization.

THE CIRCLE AND THE CROSS

The cross is not an accessory religious image: it is the geometry of living together. To fix the horizontal and the vertical is to show that unity is not the negation of opposites but their harmonic relationship. Jesus on the cross embodies this junction: horizontality of love and verticality of transformative energy, culminating in unity. The central point, the axis mundi, is the place of passage where the multiple becomes One again.

THE SACRED LETTERS: JUDAISM, CHRISTIANITY AND ISLAM

The Tetragrammaton YHWH is the architecture of a becoming. Yod (principle), Heh (manifestation), Vav (link) and Heh (return) form a structure where the double Heh signifies squaring, stabilization of a potential. Reading YHWH through trigonometry enlightens us in more ways than one: Y (Yod) corresponds to horizontality (cos x), Vav to verticality (sin x), and the repetition of the letter H is the squaring, the affirmation of a totality that cannot be reduced.

Yeshua (יֵשׁוּעַ) reveals the same mechanics: Yod-Shin-Vav (Ayin, the vowel disappears in written Aramaic). Shin is the flame, the active purification of the Word; Vav is the nail that connects high and low; Yeshua is therefore the divine seed traversing fire and connecting heaven and earth. The two-triangle star (ISIS + RA = EL, ISRAEL) visually manifests the reunion of polarities: two triangles that interpenetrate and form a perfect unity. The bain-marie—a foundational image—unites water and fire, proof that transformation is the conjunction of elements, not annihilation.

IBN ARABI AND THE UNITY OF BEING

Sufism affirms without detour: the world, with its multiplicity, is the language through which the Unique reveals itself. Letters are not simple signs; they are creative forces. Complete humanity is that which reunites within itself the different letters and names, becoming the receptacle of the Word. He explains that letters are the bodies of the Divine Names and the very substance of creation. Each letter is a degree of this divine manifestation. "Know that the letters are, in their essence, the bodies of the Divine Names... All existence is a word uttered by God, and the letters are the roots of all manifested things, for it is through them that the divine word has diversified and unfolded in the universe." The perfect human being (al-insān al-kāmil) is one who understands and reunites all these letters, thus becoming the totality of the divine Word and the receptacle of all Names. This is the meaning of the Perfection and Unity sought (Tawhid). Islam possesses an unsuspected spiritual depth, far from the image of the evil bearded throat-slitter they want to sell us...

The formula cos²x + sin²x = 1 is the formal demonstration that this plurality holds within the perfect unity of the circle. He maintains that Tawḥīd is Wihdat al-Wujūd (the Unity of Being): there is only one true reality, which is God. The world, in its apparent duality and multiplicity cos²x + sin²x, is only the manifestation (the expression) of this single divine Essence.

CONSEQUENCE FOR ECONOMICS

The collapse of systems that forget unity is inevitable. Our financial and political systems have ignored sacred geometry. Linear accumulation—the flight toward infinity on a finite Earth—is a logic of implosion. We must stop thinking GDP and replace it with GNH, Gross National Happiness, as Bhutan has done. Where traditional wisdom proposes encounter and balance of polarities, our ideologies have institutionalized polarization, transformation through violence, disunion, war of all against all. The result is visible: cycles of crises, ideological skirmishes, moral collapses and finally, world wars.

The irrational constants (√2, π, φ, e) are not abstract curiosities: they testify to the infinite inscribed in form—the irrational order that sustains creation. The quest for unity is indeed the common chorus of traditions. It does not require uniformization, but the recognition and respect of diverse paths leading to the same center. To refuse this is to transform spirituality into totalitarian ideology; to accept this is to restore the plural richness of traditions while affirming the same central truth.

CLARIFICATION AGAINST DISTORTIONS

The great unity at the heart of religions is not synonymous with uniformity. True spiritual work consists in defending and preserving singularities, respecting rites and forms, preventing a great globalist synthesis from becoming an empty "mixture" that will fail anyway. My purpose has always been to show that the convergence of religious roots does not lead to a global dogma, but to mutual recognition and common responsibility toward the sacred.

CONCLUSION: RECONQUERING BALANCE

The formula cos²x + sin²x = 1 is a simple and energetic rule: the sum of polarities is unity. Any science, any social practice that deviates from it exposes itself to rupture. This is not about replacing economics with a mystical creed, but about integrating geometric and symbolic wisdom at the heart of collective choices.

After the great massacres to come (generalized hatred), we will finally be able to relearn to love one another. This is the message of Yeshua/Jesus/'Îsâ, and it is the only one that matters.